We can help if you are more specific in the questions, show us what you have already done, and let us know what you are having difficulty with. The board is not here to provide free answers to your homework.

I assume it will be an electric motor with a cable pulling the elevator some how? How heavy is the load? How big is "miniature"? No hydraulics? Does it need to have a brake if the cable breaks? I assume it has to stop at each floor?

Are you allowed to bore a hole from center of lift down to a depth of 4 floors? Then could use a length of all-thread with a rotating nut to simulate a hydraulic system. Might start by making a list of all of the functions required, then weed out all gold plate.